Refer to the previous exercise.
a. Based on the prediction equation, when the defendant is black and the victims were white, show that the estimated death penalty probability is 0.233.
b. The model-estimated probabilities are 0.011 when the defendant is white and victims were black, 0.113 when the defendant and the victims were white, and 0.027 when the defendant and the victims were black. Construct a table cross-classifying defendant’s race by victims’ race and show the estimated probability of the death penalty for each cell. Use this to interpret the effect of defendant’s race.
c. Collapse the contingency table over victims’ race, and show that (ignoring victims’ race) white defendants were more likely than black defendants to get the death penalty. Comparing this with what happens when you control for victims’ race, explain how Simpson’s paradox occurs.